Perturbations of quadratic centers of genus one
Copyright policy )Perturbations of quadratic centers of genus one
We propose a program for finding the cyclicity of period annuli of quadratic systems with centers of genus one. As a first step, we classify all such systems and determine the essential one-parameter quadratic perturbations which produce the maximal number of limit cycles. We compute the associated Poincare-Pontryagin-Melnikov functions whose zeros control the number of limit cycles. To illustrate our approach, we determine the cyclicity of the annuli of two particular reversible systems.
28 pages
34C07 (34C05 37G15), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 34C07, 34C08
34C07 (34C05 37G15), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 34C07, 34C08
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